Modulation of contact resonance frequency in friction force microscopy on the atomic scale

Friction is one of the physical phenomena, which maybe is one of the greatest challenges to the
scientic and industrial communities and has a direct linkage to energy eciency and environmental
cleanliness of all moving mechanical systems. In everyday life, one rarely thinks about friction or
appreciates its importance, but there is no doubt that it is a major cause of energy loss. Hence,
the prospect of further understanding and reducing friction in engineering systems has real-life and
economic implications for not only preserving our limited energy resources, but also in saving our
planet from hazardous emissions for generations to come.
On the macroscopic scale, the da Vinci-Amonton laws are common knowledge (1. friction is
independent of the apparent contact area, 2. friction is proportional to the normal load and 3. fric-
tion is independent of velocity). With the invention of the Atomic Force Microscope in 1986, a
modern eld of tribology developed which made it possible to investigate friction on the micro-
scopic scale. Experiments with small contacts have shown that the abovementioned empirical laws
are not always correct. Reasons may be related to a larger surface-to-volume ratio and the greater
importance of adhesion, surface chemistry and surface structure. By these means, a better under-
standing of the phenomenon of friction is required, to learn how to quantify and eventually how to
control friction.
The central topic of this thesis concerns friction on the atomic scale. With the Friction Force
Microscope, that is operated in ultra high vacuum and at room temperature, the friction of a
single asperity contact between a sharp probing tip and a
at surface has been investigated. This
is in contrast to the friction between two bodies on the macroscopic scale, where the contact is
formed by a multitude of asperities. This single asperity is dragged over the surface by a support.
While the support is moving with constant velocity, the tip apex itself typically exhibits a stick-slip
motion, where the tip periodically sticks in a potential well, until the pulling force is high enough
to overcome the static force and to induce a slip event, where the tip jumps into an adjacent
potential well. The stick-slip process has been studied and analysed profoundly by experiments
and numerical calculations by means of the tip motion on the surface lattice, also with respect of the limit cases of the superlubricity regimes.
The in
uence of the applied load on the stick-slip motion was experimentally and numerically
investigated and indicates that the friction force is decreasing when reducing the load, until the load
reaches a critical threshold, below which the system enters the superlubricity regime. Numerical calculations indicate that a reduction in load enlarges the stability regions, where the tip apex
position is in a potential well, and thus facilitates the tip to follow a trajectory with lower energy
barriers.
The eect of mechanical actuation of the cantilever on friction has also been analysed experimen-
tally and numerically. Numerical model calculations have been performed in two dimensions based
on an integrator solving the Newton equation of motion. For the actuation in normal direction, the
stability regions are shown to periodically expand and contract, and similar to a decreasing load
allows the tip trajectory to explore regions on the potential energy surface with lower energy barri-
ers. Mechanical actuation of the cantilever in normal direction was already shown experimentally
by others to reduce the friction, an actuation of the torsional vibration mode is now demonstrated
to also reduce the friction force.
The in
uence of the temperature on the stick-slip motion is investigated numerically by im-
plementing Brownian motion of the tip apex, and indicates that the thermal noise allows the tip
apex to overcome an energy barrier on the potential energy surface slightly earlier compared to
the case at zero temperature and thus reduces the friction force. An increasing temperature is
shown to decrease friction until a critical temperature is reached, above which the system enters
the superlubricity regime, similar to the load and actuation dependence of friction.
The tip trajectory has been analysed in detail by numerical and analytical calculations with
subject to the scan direction and oset, which allows to describe and quantify the angular de-
pendence of static and kinetic friction for square and hexagonal lattice symmetries. Since the tip
trajectory is not directly accessible in experiments, a method has been introduced which combines
the horizontal and vertical de
ections to determine the tip path also in experiments. Hence, several
aspects of the stick-slip process were analysed thoroughly, which give new insight and an improved
understanding of the friction on the atomic scale.
The second important topic of the thesis concerns resonance frequencies of a cantilever in
contact. The contact resonance frequency depends on several parameters such as load, contact
area, material properties of the tip apex and sample material, and can be measured and tracked in the experiment. The rst mode of the normal and torsional contact resonance frequencies indicate
a maximum when the contact is not stressed in the lateral direction. The contact resonance
frequencies are decreasing shortly before a slip event, around which the contact resonances drop to
its initial values, but can not be accurately followed, owing to the nite phase locked loop response
time. Thus, the contact resonances may be used as an indicator of a forthcoming slip event.
Such a behaviour might also be relevant for macro-slip events, such as earthquakes, where early warning systems are still missing. The contact resonance technique also appears to be sensitive
to atomic defects. Atomic defects are detected for the normal and torsional modes, which are not
clearly detected in the lateral force or in the vertical de
ection channels. Additional excitation
of the sliding system at the contact resonance reduces the friction and gives further informations
about the mechanical properties of the asperity contact and the sample material. Since the contact
resonance frequency of the normal and torsional mode oscillations are tracked simultaneously to
the lateral force, a contact resonance map is generated in addition to the friction force map, which
is presented on the atomic scale for the rst time.
In summary, several aspects of friction, especially the stick-slip process, and contact dynamics,
including the contact resonance frequencies, have been thoroughly investigated on the atomic scale.